ELECTRONS AND PHONONS IN HIGH TEMPERATURE SUPERCONDUCTORS

Abstract

The era of conventional superconductivity (CSC) begins with Kammerlingh's discov-ery in 1911 while that of high temperature superconductivity (HTSC) was heralded in 1986 with the breakthrough discovery of Bednorz and Muller. These historic land-marks made this phenomena one of the most exhilarating and fascinating field of condensed matter physics. A huge bulk of experimental and theoretical literature has been produced to understand the mechanism and properties of sup econductors during the last century and the quest is still on. The long pending intricate problem of anharmonic phonon-electron problem, in HTSC gained heightened interest with time among condensed matter physicists with the fact that anharmonicity is responsible for many different properties of solids. Of the several proposed mechanisms of HTSC it is always suspected that it is the phonon that helps to join the electrons into superconducting pairs, i.e., the dressing of electrons with phonons in the form of polarons, bipolarons, etc., reinvigorated the concept of attractive interaction between electrons (pairons or cooper pairs). Some of the remarkable investigations reveal that the anharmonicity of less than 1% can induce superconductivity even in the presence of coulomb repulsion which inspired us to take up this exciting issue on new grounds. Further, the effects of disorders and defects are well known which drastically change the frequency (energy) spectrum of 11 solids may also play decisive role in understanding the problem in a wider perspec-tive. The simultaneous and exact treatment of both impurity and anharmonicities is, however much complicated but cannot be overlooked, because (i) the anharmonicity perturbation is never small (phonon wave function are highly influenced by the an-harmonic potential), (ii) defects invoke the impurity (gap, local or resonance) modes which effectively alter the symmetries (loss of inversion symmetry) and (iii) presence of anharmonicity and localized fields give rise to the impurity- anharmonicity interac-tion modes. With the advent of HTSC YBa2Cu307_6 emerged as representative high temperature superconductors (HTS) (cuprates) with amazing dynamical properties, namely; (a) presence of nodes in the energy gap (ds2_0 pairing) that leads to an ex-cess of excitations at low temperatures (evidenced by transport experiments), (b) the temperature dependent London penetration depth, (c) the infrared and Raman scat-tering experiments, (d) Josephson tunneling and thermodynamic measurements, (e) the d-wave symmetry as addressed by pairing mechanisms like magnetic interactions, spin fluctuations (f) spectacular behavior of thermal conductivity(THC) near 7', re-gion and (g) the temperature dependent NMR relaxation rates infer the evidence of spin-singlet pairing with s-wave or d-wave symmetry. The vibration of apical oxygen (04) ions along the c—axis in YBaCuO exhibit strong influence of anharnionicity and microscopic examination, however, reveals that nearly all YBaCuO materials contain defects and these structural defects have been seen in high-resolution TEM. The discovery of HTS in cuprates was actually inspired by possible strong electron-phonon(ep) interaction in oxides owing to polaron formation or in mixed-valence systems. Shortly after the discovery, several experiments lead some people to believe that ep coupling may not be relevant to HTSC. Instead, strong electron-electron cor-relation has been proposed to be the mechanism of high-T, superconductivity. This approach is attractive since d-wave pairing is a natural consequence. Furthermore, the HTS evolve from antiferromagnetic insulating compounds where the electron-electron interactions are strong. To study dynamical properties and the microscopic phenomenon, the Quantum 111 dynamics of electrons and phonons is earmarked adopting the method of double time thermodynamic Green's functions as state of the art methodology via an almost com-plete crystal Hamiltonian (without using BCS Hamiltonian) which comprises of the effects due to electrons, phonons, impurities, anharmonicities and interactions thereof. In this new frame work the phonon density of states(PDOS) and electron density of states(EDOS) have been investigated via non-perturbative approach. The vari-ous peaks observed in our model calculations for YBa2Cu307_5 and La2_zSrxCu04 crystals show excellent agreement with the experimental data with several additional peaks in diagonal PDOS, non-diagonal PDOS and total PDOS have been predicted in the theory as futuristic experiments. In the present model the behavior of renor-malized frequency coke depicts the similar results of appearance of energy gap (with anisotropic character) and functional dependence of dx2_g2 wave pairing in the su-perconducting state in cuprates as reported in the well established works showing the co-existence of s- and d- wave symmetry along the [110] direction in the k-space and is well supported by the experimental observations. The presence of ep coupling constant in all constituent terms of PDOS establishes its importance in determining the dynamical properties of superconductors. The investigated expressions of EDOS in the new framework are found responsible to describe the direct information about the angle-resolved photoemission spectroscopy (ARPES) experiments. In the present study the electron-phonon interaction induced with impurity shows the evidence of four-fold symmetric quasiparticle 'cloud' intensity peaks aligned with the nodes of the d-wave superconducting gap which is believed to characterize superconductivity in HTSC materials and supports well the ARPES and spectroscopic imaging scan-ning tunneling microscopy (SI-STM) experimental predictions. The interactions of electron give rise to anharmonic modes, impurity modes and impurity-anharmonicity interference modes. These investigations show that the localized anharmonic phonon-electron interac-tion is essentially a novel many body problem in HTSC studies and motivated us to study the transport properties (e.g, thermal conductivity (THC)) of HTS which has iv been emerged as a probe to provide a deep and detailed understanding of the nature of lattice vibrations, electronic states and scattering processes in HTS. The outcome of theoretical and experimental studies of THC of HTS gained heightened interest to provide better insight into the intricate mechanism of the phenomenon.Two contem-porary models on THC pioneered by Bardeen, Rickayzen and Tewordt (BRT) (later on extended by and Callaway (Which supports well the Kubo model) greatly inspired the successors to work on the numerically amenable models with better understanding of scattering mechanisms via relaxation time approximation, energy scenario of solids and allied problems. However, BRT model is mainly aimed to consider the energy transport associated with the flow of charge carriers which is referred to as electronic THC ne (of superconductors) where as the latter undertakes the study of heat carried out by phonons and is known as lattice THC kp of most of the crystalline solids. The THC ,c e tcp of HTS in the vicinity of transition temperature emerged as a center of experimental and theoretical attention to explain the spectacular dip in this domain. Out of sufficient experimental and theoretical works, efforts have been made to explain the crucial dip region but a successful explanation could not come up. At fairly low temperatures the Widemann-Franz law often breaks down severely and suggests that IQ starts to disappear leaving only kp. Hence instead of considering ice and ti-,p separately (instead of isolated channels), the concept of analyzing total heat conductivity R, kp is found reasonably correct. The exact treatment of THC of solid is hampered due to the mathematical ambiguity of Boltzmann's transport equation, lack of knowledge of phonon dispersion and the anharmonic forces, inadequate use of Matthiessen's rule inaccessible from most of the models have been removed by introducing the equivalence of relaxation time and electron (phonon) line widths. The identification of pairing mechanism and theory of ep-interaction in presence of strong electron correlation in HTS is still an outstanding issue whereas there is a large body of experimental evidences on strong ep- coupling. We strategically sepa-rated the problem in different temperature regimes and tried to develop a heuristic understanding of these experimental data. The analysis of THC of HTS is carried out V by taking into account the contribution from combined boundary, impurity, phonon-phonon, interference, resonance scattering and the ep- scattering term which found to be most prominent for the physics of THC of HTS and equally supports the concept of formation of pairons, as in BCS theory. In the transition region the play of electrons and phonons appear to be important when they contribute to the pairon sea (super-conducting condensate) instead of heat transport naturally affecting THC (since the pairons do not contribute to the entropy). The anharmonic phonon-electron problem thus investigated successfully explained the transport phenomena in this region and resolved the long pending proble